Ever since the very first model of the process by Bohr and Wheeler
[1]}, fission has always been thought of as an extreme deformation
process. This concept is very easily built in phenomenological approaches based
on the liquid drop model. However, since the nuclear Hamiltonian \(\hat{H}\)  is
invariant under rotations, the nuclear wave functions \(\mathinner {|{\Psi }\rangle }\)  should also
be rotationally invariant and characterized by good angular momentum. Clearly,
this is not compatible with the concept of deformation. This could pose
interesting conceptual difficulties if fission were described with
ab initio methods; in the context of the EDF approach, deformation is in
fact a natural consequence of a phenomenon called spontaneous symmetry
breaking [2]}, [3]}. When solving the Hartree-Fock or
Hartree-Fock-Bogoliubov equation of the single-reference EDF theory (see
below), solutions that break some or all of the symmetries of the nuclear
Hamiltonian can lower the energy of the system. This effect, also known as the
Jahn-Teller effect, is present in many fields of physics, from nuclei to
electronic systems to quantum field theory; see [4]} for a
discussion in the context of nuclear physics.
